The perception of dynamic events appears to be guided by the underlying mathematical structure of objects moving through space and over time. Previous research on the perception of: (a) how people walk, (b) how wheel-like objects roll, (c) how the human head changes during growth and aging, (d) how texture gradients change when one moves through space, and (e) how birds navigate by the movement of the stars, all point towards a grammar of dynamic events. Central to this grammar is a functional mathematical point, which we call the center of moment. This point around which all parts of the moving (or changing) object maintain a constant relation. Most importantly, however, is that in the five events mentioned the center of moment is perceptually useful: For a walker it can determine gender, for a tumbling object it can determine how wheel-like it appears, for an aging head it determines the goodness of various profiles as representing older and younger individuals, for texture gradients during egomotion it determines the direction towards which one is moving, and for celestial navigation it determines the location of the celestial north pole. Thus, we have at least five events that can be analyzed in this manner. In an effort to understand how we perceive constancy during movement and change, this proposal entails three interrelated projects focusing on perceptual events and their centers of moment. In the first project a detailed set of experiments is outlined on the perception of rotary motion, following up our previous research. Critical variables include configuration of lights mounted on a wheel, irregular shapes mounted there, relative translation of the wheel as its rotates, eye movements, incoherence within the light system, and various alternative response measures to the rating scale used in the past. The second project concerns the perception of biological motion and change, and looks at categories and boundaries of movement, kinematics vs dynamics, the perception of hand gestures, and continued work on the perception of faces. The third project concerns the perception of underlying grammatical complexity in events in which event structures are varied and interwoven. Overall, these three projects lend themselves to a better understanding of how we perceive events, with a goal of forming a dynamic geometry of perception.